Which of the following numbers is a factor of 84? ${5,8,10,11,14}$
Answer: By definition, a factor of a number will divide evenly into that number. We can start by dividing $84$ by each of our answer choices. $84 \div 5 = 16\text{ R }4$ $84 \div 8 = 10\text{ R }4$ $84 \div 10 = 8\text{ R }4$ $84 \div 11 = 7\text{ R }7$ $84 \div 14 = 6$ The only answer choice that divides into $84$ with no remainder is $14$ $ 6$ $14$ $84$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $14$ are contained within the prime factors of $84$ $84 = 2\times2\times3\times7 14 = 2\times7$ Therefore the only factor of $84$ out of our choices is $14$. We can say that $84$ is divisible by $14$.